It's the circuit that matters more. You have to be able to charge the cap much quicker than it bleeds.

There must be some other physical events that you could use. With radar and a CRT display you 'see' the return time as distance along a sweep trace. On our 1950's sets the minimum was about 250 meters because the outgoing pulse took that long but 500 m travel time (out and back) when light moves about 300,000,000 m/s is just over 1 usec, and we could tell 10 m differences in range easily.

Maybe you could invert the delay, have that interval cut from something bigger that's known or some way take a ratio with a known and get a measure from that?